The present invention relates generally to methods for determining physical properties of micro-machined cantilevers used in cantilever-based instruments, including atomic force microscopes (AFM's), molecular force probe instruments and chemical or biological sensing probes. It also involves using cantilevers characterized with such methods to measure fluid flow rates.
Calibrating the sensitivity of cantilevers used in cantilever-based instruments is critical for correctly interpreting the results obtained from such instruments. The foundation of this calibration is the determination of the optical sensitivity of the cantilever, the relationship between deflection of the cantilever and movement of the tip of the cantilever in the z direction. For this purpose, deflection of the cantilever is measured with the optical detection means common in such instruments, a position sensor collecting light reflected off the back of the cantilever. Knowing the optical sensitivity of the cantilever, the spring constant of the cantilever may be readily calculated.
The conventional methods for determining optical lever sensitivity have either been destructive or required that the lever be brought into hard contact with a well defined rigid surface. Because the distances are typically less than one micron, and the relative positions of the cantilever tip and such a surface difficult to locate, making such contact is far from a trivial proposition. The difficulty of the procedure is enhanced by the fact that slippage of the tip laterally over the surface introduces serious errors.
Even if the conventional methods were easy of execution, there are many instances when it is not desirable or convenient to measure optical lever sensitivity by touching a surface. When the results depend on chemical or biological sensitization of the cantilever tip, or if the tip is particularly sharp, hard contact or any contact before performing the experiment may compromise the results. Similarly compromising may be hard contact when the sample is coated on the surface and is a soft material such as cells. Finally, in the case of chemical or biological sensing probes, there may not be a rigid surface anywhere near the cantilever against which to press.
Two methods for determining optical lever sensitivity not requiring hard contact with a well-defined rigid surface have been proposed, but each has important limitations and is as yet untested. D'Costa and Hoh proposed estimation of optical lever sensitivity by moving the spot across the position sensor a known distance. Because it is not sensitive to actual motion of the cantilever, this method does not account for differences in cantilever geometry or changes in the alignment of the spot on the lever. These issues become even more critical as the length scale of cantilevers shrink. Sader proposes to rely on a plan view of the lever and the measured resonant frequency and quality factor to estimate optical lever sensitivity spring constant.
Although there has been a large amount of work dedicated to the cantilever calibration issue, the precision of the resulting techniques seems to be limited to 10%. In this situation, it is desirable to make use of another method to check for consistency.